Einstein-Straus problem in higher dimensions

摘要

Years ago Einstein and Straus (ES) showed that it is possible to match a static Schwarzschild region to an external expanding Friedmann universe. This model is extended in this work to a spacetime of arbitrary dimensions. Frequency shift of radiation coming from the boundary of the two spacetimes is calculated. Depending on the relative magnitude of gravitational and doppler effects our model gives both blue shift and red shift. The dynamical behaviour of the boundary is investigated and it is found that like the ES case our model is also unstable against small perturbation. [References: 16]